D. J. Hartfiel, Professor
Personal
- Office: Milner 210
- Telephone: Office 845-2833, Home 693-1334
- E-mail: hartfiel@math.tamu.edu
- Photo: My wife and I
Education
- B.S. Southwest Texas State University (academic scholarship)
1962
- M.S., Ph.D. University of Houston (Teaching assistantship,
research assistant, NASA traineeship) 1966, 1969
Research Interests
Matrix Theory and Computations (Basic interest in systems with
imprecise data). Recent papers are listed below. Others may be found on
MathSciNet. Preprints and reprints will be sent on request.
- D. J. Hartfiel, "Boxed iterations", to appear in Applied
Mathematics and Computation.
- D. J. Hartfiel, "Distribution of entries in a substochastic
matrix having eigenvalues near 1", to appear in SIAM on Matrix
Analysis.
- Andra Buxkemper and D. J. Hartfiel, "Understanding", to
appear in International Journal of Mathematics Education and Science
Technology.
Other Interests
- Psychology: Interest in Gestalt Theory and how this can be used in
problem solving as well as in learning. Also work on dyslexia and how, or
to what extent, this condition can be corrected.
Books/Monograph
- D. J. Hartfiel and Arthur Hobbs, Elementary Linear Algebra,
Prindle Weber Schmidt, 1987. (This is a basic book on linear algebra.)
- Darald J. Hartfiel, Markov Set-chains, Springer (LNM 1695), 1998.
ISBN 3-540-64775-9. (This monograph concerns nonhomogeneous Markov
chains in which the transition matrices are in a matrix interval. The
book should be of interest to anyone interested in Markov chain type
problems and to anyone interested in problems involving imprecise
data.)
- Darald J. Hartfiel, Matrix Theory and Applications with MATLAB,
CRC Press, 2001. (This book of 347 pages covers the basic material in
matrix theory:
#1 Review of Matrix Algebra, #2 Introduction to Vector Spaces, #3
Similarity, including the Jordan form, #4 Matrix Calculus, #5 Normed
Vector Spaces, #6 Unitary Similarity, #7 Singular Value Decomposition,
#8 LU and QR Decompostions, #9 Properties of Eigenvalues and
Eigenvectors, #10 Hermitian and Positive Definite Matrices, #11
Graphics and Topology. For insight, MATLAB is used to show pictures of
various matrix spaces, e.g. the singular matrices, and to show pictures
of solutions to differential and difference equations. Furthermore,
MATLAB is used to solve systems of linear equations, find inverses
of matrices, etc. An additional feature of the book is that at the end
of each
section there is an application of the mathematics shown in that
section. Both MATLAB and Applications work are written so that students
can do that work independently.)
- Darald J. Hartfiel, Nonhomogeneous Matrix Products, World
Scientific, 2002. (A nonhomogeneous matrix product is a product A1...Ak
where each Ai is an n x n matrix. Such products arise in constructing
curves and fractals, as well as in systems in which the transition
matrix changes at each step. This book provides basic results about
nonhomogeneous matrix products and shows how these results
can be used in graphics and in systems. MATLAB code is provided for the
applications shown in the book.)
Short Work Record
- In Rank: Assistant Professor (1969-1974), Associate Professor
(1974-1981), Professor (1981-2005 ), Professor Emeritus (2005-)
- Graduate Students with Theses: 12 Masters, 1 Ph.D. (A few
co-chaired)
- Research Papers: See MathSciNet
- Awards: 3 teaching awards